216 CHAPTER 5 Discrete Probability Distributions Lottery. In Exercises 15–20, refer to the accompanying table, which describes probabilities for the California Daily 4 lottery. The player selects four digits with repetition allowed, and the random variable x is the number of digits that match those in the same order that they are drawn (for a “straight” bet). 15. Mean and Standard Deviation Find the mean and standard deviation for the numbers of correct matches. 16. Range Rule of Thumb for Significant Events Use the range rule of thumb to determine whether 0 matches is a significantly low number of matches. 17. Range Rule of Thumb for Significant Events Use the range rule of thumb to determine whether 4 matches is a significantly high number of matches. 18. Using Probabilities for Significant Events a. Find the probability of getting exactly 2 matches. b. Find the probability of getting 2 or more matches. c. Which probability is relevant for determining whether 2 is a significantly high number of matches: the result from part (a) or part (b)? d. Is 2 a significantly high number of matches? Why or why not? 19. Using Probabilities for Significant Events a. Find the probability of getting exactly 3 matches. b. Find the probability of getting 3 or more matches. c. Which probability is relevant for determining whether 3 is a significantly high number of matches: the result from part (a) or part (b)? d. Is 3 a significantly high number of matches? Why or why not? 20. Using Probabilities for Significant Events a. Find the probability of getting exactly 1 match. b. Find the probability of getting 1 or fewer matches. c. Which probability is relevant for determining whether 1 is a significantly low number of matches: the result from part (a) or part (b)? d. Is 1 a significantly low number of matches? Why or why not? Texting and Driving. In Exercises 21–26, refer to the accompanying table, which describes probabilities for groups of five drivers. The random variable x is the number of drivers in a group who say that they text while driving (based on data from an Arity survey of drivers). 21. Mean and Standard Deviation For groups of five drivers, find the mean and standard deviation for the numbers of drivers who say that they text while driving. Number of Matching Digits P(x) 0 0.656 1 0.292 2 0.049 3 0.004 4 0+ Number of Drivers Who Say That They Text While Driving P(x) 0 0.066 1 0.238 2 0.344 3 0.249 4 0.090 5 0.013
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